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Added by
Pierfrancesco Urbani
Publication date
2020
fields
Physics
and research's language is
English
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We search for a Gardner transition in glassy glycerol, a standard molecular glass, measuring the third harmonics cubic susceptibility $chi_3^{(3)}$ from slightly below the usual glass transition temperature down to $10K$. According to the mean field picture, if local motion within the glass were becoming highly correlated due to the emergence of a Gardner phase then $chi_3^{(3)}$, which is analogous to the dynamical spin-glass susceptibility, should increase and diverge at the Gardner transition temperature $T_G$. We find instead that upon cooling $| chi_3^{(3)} |$ decreases by several orders of magnitude and becomes roughly constant in the regime $100K-10K$. We rationalize our findings by assuming that the low temperature physics is described by localized excitations weakly interacting via a spin-glass dipolar pairwise interaction in a random magnetic field. Our quantitative estimations show that the spin-glass interaction is twenty to fifty times smaller than the local random field contribution, thus rationalizing the absence of the spin-glass Gardner phase. This hints at the fact that a Gardner phase may be suppressed in standard molecular glasses, but it also suggests ways to favor its existence in other amorphous solids and by changing the preparation protocol.
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In the present work, we employ broadband dielectric spectroscopy to study the molecular dynamics of the prototypical glass former glycerol confined in two microporous zeolitic imidazolate frameworks (ZIF-8 and ZIF-11) with well-defined pore diameters of 1.16 and 1.46 nm, respectively. The spectra reveal information on the modified alpha relaxation of the confined supercooled liquid, whose temperature dependence exhibits clear deviations from the typical super-Arrhenius temperature dependence of the bulk material, depending on temperature and pore size. This allows assigning well-defined cooperativity length scales of molecular motion to certain temperatures above the glass transition. We relate these and previous results on glycerol confined in other host systems to the temperature-dependent length scale deduced from nonlinear dielectric measurements. The combined experimental data can be consistently described by a critical divergence of this correlation length as expected within theoretical approaches assuming that the glass transition is due to an underlying phase transition.
Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.
The Gardner length scale $xi$ is the correlation length in the vicinity of the Gardner transition, which is an avoided transition in glasses where the phase space of the glassy phase fractures into smaller sub-basins on experimental time scales. We argue that $xi$ grows like $ sim sqrt{B_{infty}/G_{infty}}$, where $B_{infty}$ is the bulk modulus and $G_{infty}$ is the shear modulus, both measured in the high-frequency limit of the glassy state. We suggest that $xi$ might be inferred from stress-stress correlation functions, which is more practical for experimental investigation than studying two copies of the system, which can only be done in numerical simulations. Our arguments are illustrated by explicit calculations for a system of disks moving in a narrow channel, which is solved exactly by transfer matrix techniques.
A database of minima and transition states corresponds to a network where the minima represent nodes and the transition states correspond to edges between the pairs of minima they connect via steepest-descent paths. Here we construct networks for small clusters bound by the Morse potential for a selection of physically relevant parameters, in two and three dimensions. The properties of these unweighted and undirected networks are analysed to examine two features: whether they are small-world, where the shortest path between nodes involves only a small number or edges; and whether they are scale-free, having a degree distribution that follows a power law. Small-world character is present, but statistical tests show that a power law is not a good fit, so the networks are not scale-free. These results for clusters are compared with the corresponding properties for the molecular and atomic structural glass formers ortho-terphenyl and binary Lennard-Jones. These glassy systems do not show small-world properties, suggesting that such behaviour is linked to the structure-seeking landscapes of the Morse clusters.
Fluctuations of the order parameters of the Gardner model for any $alpha<alpha_c$ are studied. It is proved that they converge in distribution to a family of jointly Gaussian random variables.
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